3.1 $B%$%s%H%m(B

$B!!%3%s%T%e!<%?!<$G?tCM7W;;$r$7$F(B ($BM-8B¹$B!#(B $B87L)2r$r5a$a$k$3$H$K$9$k$H!"@~7AJ}Dx<00J30$ONc30E*$J>u67$r$N$>$$(B $B$F2r$1$J$$(B²$B!#$7$+$7!"M-8B@:EY$N2r(B ($B6a;w2r(B) $B$GK~B-$9$k$3$H$K$9$l$P!"$+$J$jB?$/$NJ}Dx<0$,2r$1$k$3$H$K$J$k!#(B

$B!!$3$3$G$O(B$BFsJ,K!(B$B$H(B $B%K%e!<%H%s(BNewton $BK!(B$B$r(B $Be$2$k$,!"(B $B$3$l$i$O2r@O3X$N3X=,$H$b4X78$,?<$$!#(B $BFsJ,K!$OCf4VCM$NDjM}$N6h4V=L>.K!$K$h$k>ZL@(B ($BCf4VCM$NDjM}$O$$$o$f$k(B $B!VB8:_DjM}!W$G$"$k$,!"(B $B$3$N>ZL@$O!V9=@.E*$J!W>ZL@$G$"$k$H8@$($k(B) $B$=$N$b$N$G$"$k$H9M$($i$l$h$&!#(B $B$^$?(B Newton $BK!$O1"4X?t$NDjM}$d5U4X?t$NDjM}$N>ZL@$KMQ$$$k$3$H$b$G$-$k$7!"(B $B

$B

$BNcBj(B1: $BFsJ,K!$K$h$C$F!"J}Dx<0(B $\cos x - x=0$ $B$N2r$r7W;;$;$h!#(B

$BNcBj(B2: Newton $BK!$K$h$C$F!"J}Dx<0(B $\cos x - x=0$ $B$N2r$r7W;;$;$h!#(B

$B$3$NJ}Dx<0$O!"0l8+$"$^$jJ#;($G$O$J$$$,!"(B $B<0$NJQ7A$G2r$r5a$a$k$3$H$OFq$7$$!#(B $B0lJ}!"2r$NB8:_$r<($9$3$H$OHf3SE*4JC1$G$"$k!#(B $B $f(x) :=\cos x - x$ $B$H$*$$$F!"(B $f$ $B$r>/$7D4$Y$F$_$l$P!"(B $B$3$NJ}Dx<0$K$O$?$@(B1$B$D$N $B$K$"$k$3$H$,J,$+$k(B³$B!#(B $f$ $B$N%0%i%U$N357A$O!"Bg;(GD$K8@$&$H!"(B $y=-x$ $B$r%5%$%s!&%+!<%VIw$KGHBG$?$;$?$b$N$K$J$k!#(B $B%3%s%T%e!<%?!<$GIA$$$?%0%i%U$r8+$l$P!"(B $f(x)=0$ $B$,M#0l$N

$B%3%s%T%e!<%?!<$GJ}Dx<0$r07$&>l9g!"(B $B%3%s%T%e!<%?!<$J$i$G$O$N$d$jJ}$,$"$k!#(B $BM-8B2s$N7W;;$G??$N2r(B ($BL58B@:EY$N2r(B) $B$r5a$a$k$3$H$O$"$-$i$a$F!"(B $B??$N2r$r5a$a$k$K$OL58B2s$N1i;;$,I,MW$@$,!"(B $BM-8B$NMW5a@:EY$r;}$D2r(B ($B6a;w2r(B) $B$O$=$3$=$3$N2s?t$N4pK\E*$J1i;;(B ($B;MB'1i;;(B) $B$G5a$^$k$h$&$JJ}K!$r:NMQ$9$k!"$H$$$&$b$N$G$"$k!#(B $B=>$C$F!"%"%k%4%j%:%`$OBgDq$N>l9g!"7+$jJV$7$N$"$k$b$N$K$J$k!#(B

$B%3%s%T%e!<%?!<$K$h$kJ}Dx<0$N?tCM2rK!$O!V7+$jJV$7!W$,%-!<(B

1. $B@~7?J}Dx<0(B (1$B $B$,Hs>o$KBg$-$$LdBj$,8=$o$l$k(B
   $BNc$($P(B N=1$B2/(B ($B86;RO'05NOMF4o$N9=B$7W;;$G$"$k$H$+(B⁴)
2. $BHs@~7?J}Dx<0$N>l9g!"LdBj$N<+M3EY$,Dc$/$F$bH?I|7W;;$K$J$k!#(B
   1. $BM-8B2s$N;MB'$G$O(B exact ($B87L)(B) $B$K2r$1$J$$LdBj$,$[$H$s$I$G$"$k!#(B
   2. $B!VH?I|K!!W$GB?$/$NLdBj$,2r$1$k!#(B
      $B$9$J$o$A!"??$N2r(B $x^*$ $B$r$"$kNs(B $\{x_n\}$ $B$N6K8B$H$7$F$H$i$((B ( $\dsp\lim_{n\to\infty}x_n=x^*$)$B!"(B $B==J,Bg$-$J(B $n$ $B$KBP$7$F(B $x_n$ $B$r(B $x^*$ $B$N6a;w$H$7$F:NMQ$9$k!#6a;w2r$G$O$"$k$,!"(B $B%3%s%T%e!<%?!<$G?tCM7W;;$9$k8B$j!"(B $BM-8B@:EY$G$"$k$3$H$OHr$1$i$l$J$$$N$G!"(B exact $B$JJ}K!(B ($B$b$7$=$l$,$"$C$?$H$7$F(B) $B$H$[$H$s$I:9$,$J$$(B⁵$B!#(B

@\2r$r7W;;$9$kJ}$,(B $B4JC1$G$"$k2DG=@-$,9b$$!#(B \qed \end{jexample}">

l9g$,$"$k (B(\textbf{$B@:EYJ]>ZIU$-?tCM7W;;(B})$B!#(B \end{enumerate}\end{jremark}">